There are many models of power chairs that fold up and break down into several pieces, making them easier to transport. Examples include Hoveround, Rascal and Go Go Travel Mobility. Each company provides the dimensions of the folded chair.
According to Family Education Network, airline regulations vary regarding power chairs and mobility devices. For example, United Airlines indicates that they may be checked with luggage, but also notes that in some cases collapsible wheelchairs may be stowed in the cabin. Southwest will store them in the cabin of the aircraft provided there is enough space.
Family Education Network indicates that if a wet cell battery powers the chair, the battery must be removed prior to storing it in accordance with federal regulations regarding hazardous materials.
It may be helpful to notify the airline in advance and to arrive early. Southwest, for example, suggests arriving as much as an hour before the scheduled departure so the chair can be prepared for storage on the plane.